According to the UM COVID-19 dashboard, 96% of faculty have self-reported as fully vaccinated.

1.) Let X = the number of fully vaccinated UM faculty in a random sample of 200. Which of the following models is the appropriate model to compute probabilities of X?

a.) Normal (192,2.77)

b.) Normal(0.96, 0.0139)

c.) Binomial(200, 0.96)

d.) Binomial(200, 0.5)

2.) Suppose we are now planning to take random samples of 800 UM faculty instead of 200 and considering the sampling distribution of the corresponding sample proportions.

What effect, if any, does this increase in sample size have on the mean of the possible sample proportion values?

a.) increases

b.) decreases

c.) stays the same

3.) Again, suppose we are now planning to take random samples of 800 UM faculty instead of 200 and considering the sampling distribution of the corresponding sample proportions.

What effect, if any, does this increase in sample size have on the standard deviation of the possible sample proportion values?

a.) increases

b.) decreases

c.) stays the same